PhD Defense Ulises Bercovich Szulmajster

Title: Deconstructing and Constructing Linkage Disequilibrium

Abstract: 

 Linkage disequilibrium (LD), the non-random association of genetic variants, is a central concept in population genetics. It provides insight into evolutionary forces such as migration, selection, and recombination, and plays a crucial role in the preprocessing of genomic data for downstream analysis. This motivates the need to better understand the components of LD, as well as to develop methods to construct and process LD matrices in ways that are both accurate and scalable.
 The thesis begins with an introduction to the area of genomics, followed by a review of the key principles of population genetics that appear throughout the work. It concludes with a focused section about LD: how it is measured, its biological and statistical
properties, and its wide range of applications. This chapter provides the technical and conceptual foundation required to understand the biological phenomena and methodological developments addressed in the manuscripts.
  The first manuscript investigates the relationship between LD and population structure. We introduce a population-structure-aware measure of LD that explicitly accounts for admixture of ancestral subpopulations. Its theoretical properties are studied, and we demonstrate its practical importance in applications such as principal component analysis, LD pruning, and LD clumping, where traditional LD measures can lead to biased results.
 The second manuscript focuses on the positive semi-definite (PSD) property of LD matrices, which ensures numerical stability in genome-wide association studies. Sparse representations of LD, commonly used for scalability, often lose this property. We develop a highly scalable approach to reconstruct sparse LD matrices that are guaranteed to remain PSD while maintaining accuracy, which grants both efficiency and stability in downstream analyses.
  The third manuscript addresses LD estimation in small sample sizes, where standard estimators are known to be biased. Using forward modeling and calibration, we design a non-parametric procedure that improves the accuracy of LD estimates compared to existing approaches. We further show that this calibration enhances performance in LD pruning, particularly in extreme scenarios with very limited sample sizes.

The defence is conducted as a hybrid defence.

To attend the digital defence, please follow the link:

https://ucph-ku.zoom.us/j/7056664710?pwd=m4oUtasUBMHVp37cKqaFQCWBaQrufy.1&omn=62264975155

Instructions if you wish to attend the defence via the digital solution: Please follow the link and hereafter the instructions to download the required -client. If the -client is incompatible with your pc, smartphone etc. you can attend via an Internet browser. Log-in in due time before to allow time to install the -client.

Ask for a copy of the thesis here: ubs@math.ku.dk or ulibercovich@gmail.com

Supervisor: Professor Carsten Wiuf, University of Copenhagen

co-supervisor: Professor Anders Albrechtsen, University of Copenhagen

Assessment Committee:
Professor Ida Moltke (chair), University of Copenhagen
Professor Asger Hobolth, Aarhus Universitet
Professor Garreth Hellenthal, University College London